The Cauchy problem for nonlinear quadratic interactions of the Schrödinger type in one dimensional space

DOI10.1063/1.5045337zbMath1398.35212arXiv1704.00862OpenAlexW2884703658MaRDI QIDQ4583083

Isnaldo Isaac Barbosa

Publication date: 27 August 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.00862

zbMATH Keywords

Cauchy problemnonlinear opticsglobal well-posednessI-methodcoupled Schrödinger equations

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Related Items (2)

On global existence of L2 solutions for 1D periodic NLS with quadratic nonlinearity ⋮ Well-posedness and lower bounds of the growth of weighted norms for the Schrödinger-Korteweg-de Vries interactions on the half-line

Cites Work

• Unnamed Item
• Sharp bilinear estimates and well posedness for the 1-D Schrödinger-Debye system.
• The Cauchy problem for a Schrödinger-Korteweg-de Vries system with rough data.
• Stability of solitary waves for a system of nonlinear Schrödinger equations with three wave interaction
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On the Cauchy problem for the Zakharov system
• Multilinear estimates for periodic KdV equations, and applications
• On a system of nonlinear Schrödinger equations with quadratic interaction
• Stability Analysis of Multipulses in Nonlinearly-Coupled Schrodinger Equations
• Global Well-Posedness for Schrödinger Equations with Derivative
• Well-posedness for the Schrödinger-Korteweg-de Vries system
• Quadratic forms for the 1-D semilinear Schrödinger equation
• Periodic pulses of coupled nonlinear Schr\"odinger equations in optics

This page was built for publication: The Cauchy problem for nonlinear quadratic interactions of the Schrödinger type in one dimensional space